In the past, exposure apparatus using X-rays has attracted attention for use as lithographic-exposure apparatus used in the manufacture of semiconductor devices and other products. When using X-rays as exposure light, since there are no X-ray-transmissive optical materials or refractive optical materials that can be used for making lenses, a reflective mask is used. Also, the projection-optical system is a reflection-type projection-optical system. One conventional type of reflection-type projection-optical system usable in exposure apparatus employing X-rays as the exposure light comprises eight reflective mirrors, such as disclosed in U.S. Pat. No. 6,710,917 (corresponding to Japanese Laid-Open Patent Document No. 2002-139672).
In the conventional projection-optical system disclosed in the '917 patent, the image-side numerical aperture (NA) is 0.4. But, it would be desirable to increase the image-side NA further to achieve higher resolution. In addition, this conventional projection-optical system comprises reflective mirrors having aspherical reflecting surfaces having extremely large absolute values of center radii of curvature. Effective methods for inspecting such surfaces, for surface-shape errors, do not yet exist. Currently, the most effective inspection method utilizes the principle in which light that has passed through a pinhole is reflected by the aspherically-shaped reflective surface. But, surface-shape errors cannot be inspected and detected with the desired precision unless the absolute value of the center radius of curvature of the reflective surface is less than a certain value.